Technical Field
The present invention relates to pattern recognition and more particularly to systems and methods for recognizing and restricting lithographical patterns for integrated circuits.
Description of the Related Art
With shrinking features sizes (technology nodes), the number of integrated circuit (IC) layout patterns printed within a photon radius increases. This has multiple effects on printability quality of the patterns on a wafer, and in effect in the yield of the chips manufactured. High yield is a definitive requirement for a financially viable chip manufacturing process. A strategy to address this limiting yield problem is to restrict the number of allowed layout patterns to the ones with increased probability of printability success. For example, it is expected that in a 22 nm technology node, the number of possible patterns will be in the order of 1024. The number of allowed patterns is expected to be in the order of 106.
A major step in this direction is the identification of those patterns. To accomplish this, one needs to have pattern identification, matching and classification algorithms that can respectively identify all different patterns of a specific size, match them to existing ones and finally classify them into similarity classes according to specific criteria. The classification will finally reveal the minimal set of patterns for the inclusion in the 22 nm technology node.
In the area of lithography, pattern matching has been used for other applications, e.g., OPC (optical proximity check), and hotspot detection. However, these algorithms are not sufficient to cover the needs of the present problem. In particular, there are two prior solutions, namely the L3GO and the Walsh approaches. L3GO uses geometric structures, called glyphs, to describe patterns and then uses graph techniques to map similar patterns. One of the major limitations of this approach is that it requires prior knowledge of the pattern, so pattern identification is not possible. Also, it is very tedious to describe a pattern, limiting its applicability and scaling. Finally, it does not enable projecting the patterns into a 2D space which eases classification.
The Walsh approach uses Walsh filters to decompose an image. It then uses the coefficients of the decomposition to map the pattern into a 2D space and a k-means distance metric to classify them. The number of the Walsh coefficients depends on the window size. For a 4 by 4 pixels window, we have 16 coefficients. As we scale down in technology, the window sizes increase significantly and thus the Walsh approach faces scaling limitations.
A different approach uses aberrations (the inverse Fourier transform of the optical path difference function) of patterns and does exact match pattern matching (correlations) to identify hot-spots. This approach is proven to be very fast, but reaches limitations when the window sizes increase. In addition, due to the fact that it does exact match, it faces the same restrictions as with L3GO. Other approaches use graph theory, similar to L3GO, to identify hot-spots and thus have similar limitations.
Another approach splits the patterns into vertices and edges and defines contour signatures. Based on these, it classifies the patterns into contour equivalence classes. This again is a very different approach and suffers from problems with scaling.
Wavelets have been used widely in image and video processing for pattern matching. In lithography, wavelets have been used in mask design and OPC. In another approach, they define a wavelet penalty function to minimize the mask complexity. In this approach, they split the patterns into segments and apply Bessel-like wavelets, get the decomposition coefficients to use them as parameters in the least square metric they define to correct the patterns. Other approaches use wavelet edge moments to define an image signature and then uses the Euclidean distance metric to retrieve similar images from a database. This approach uses the cubic wavelet and a variable number of wavelet maxima moments (moments of edges of images). These approaches suffer from scalability issues and complexity issues.